With the recipe for the iterative procedure, we use the theoretical pair correlation function of phase singularities in random waves [1]} to retrieve their effective interaction.
We perform the retrieval considering in parallel both cases of same and opposite topological charge interaction.
Typically the mean-field potential is a good choice as a starting guess of the interaction potential \(V^{(0)}(r)\)  [2]}.
Including the topological charge, there would be two mean-field potentials:
\(V^\mathrm {mf}_\mathrm {same}(r) = -\log \,[g_\mathrm {same}(r)],\quad V^\mathrm {mf}_\mathrm {opp}(r) = -\log \,[g_\mathrm {opp}(r)],\) 
